Functions-6

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Let A ⊆ N and f : A → A be defined by
f(n) : the highest prime factor of n.
If range of f is A, determine A. Is A uniquely determined?

Solution: For any n ∈ A, we have

f(n) = Highest prime factor of n

=> Range of f consists of prime number only

But, it is given that range of f is A. Therefore, set A consists of prime numbers only.

Hence, A = set of some prime numbers.

Clearly, A is not uniquely determined.

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